Method for transmitting a binary information word

ABSTRACT

A method is for transmitting a binary information word (MI) coded on r bits to which is attached a redundancy (CRC) coded on s bits, s and r being integers. The redundancy (CRC) signals the appearance of erroneous bits after the transmission, and is obtained by carrying out a Euclidian division of the information word (MI) to be transmitted by a generator polynomial coded on at most s bits. The generator polynomial is chosen so that it satisfies at least one of the following conditions, namely that the Hamming weight of the multiples of the generator polynomial is greater than or equal to a chosen threshold, or the generator polynomial allows the detection of at least 2 s-1 −3 consecutive erroneous bits.

FIELD OF THE INVENTION

The invention relates generally to the transmission of binaryinformation words, and, more particularly, to the detection of erroneousbits of these information words after the transmission.

BACKGROUND OF THE INVENTION

Conventionally, a CRC (“Cyclic Redundancy Check”) code is used to detecterroneous bits in the information transmitted between two systems,namely a source system (emitter) and one or more receiving systems(receivers).

The emitter and the receivers are coupled by transmission circuitry thatis usually not very reliable, which may disrupt the content of theinformation transmitted. For example, an information word being writtenin the form of a bit sequence “100011011” may, on reception, become“001011011”. The values of the first and third bits have been corruptedduring transmission.

For the receivers to detect that the received information word isincorrect, a few bits called the “signature” are added to theinformation word. This signature is obtained by applying a hash functionto the information word to be transmitted, such as:

H(MI)=CRC

Where H is the hash function, MI is an information word to betransmitted, and CRC is its signature. This hash function is commonlycalled “Checksum” by those skilled in the art.

There are many functions capable of generating the signature (like theadd function). Such a checksum function is considered to be effective ifthe signature systematically indicates the appearance of an erroneousbit.

An example checksum function is called Euclidian division. Moreprecisely, the signature, also called “redundancy”, is generated bydividing the information word to be transmitted by a generatorpolynomial. The redundancy is then equal to the rest of this Euclidiandivision.

It is considered that a generator polynomial supplies an effectiveredundancy if the latter allows the detection of a maximum of erroneousbits in the received information word. The qualification of a goodgenerator polynomial then depends on the types of the most frequenterrors associated with the transmission circuitry. Mainly, there are twotypes of errors, namely independent random errors (according to theBernouilli scheme) and burst errors, in other words a certain number ofconsecutive erroneous bits.

It is particularly difficult to find a generator polynomial capable ofgenerating a redundancy allowing the detection of these errors, whetherthey be random or burst.

SUMMARY OF THE INVENTION

According to a first aspect, a method is for transmitting a binaryinformation word coded on r bits to which is attached a redundancy codedon s bits, s and r being integers. The redundancy signals the appearanceof erroneous bits after the transmission, and is obtained by carryingout a Euclidian division of the information word to be transmitted by agenerator polynomial coded on at most s bits.

According to a general feature of this aspect, the generator polynomialis chosen so that it satisfies at least one of the following conditions,namely that the Hamming weight of the multiples of the generatorpolynomial is greater than or equal to a chosen threshold, or thegenerator polynomial allows the detection of at least 2^(s-1)−3consecutive erroneous bits.

In other words, in order to generate an optimal redundancy, thegenerator polynomial may satisfy at least one of the two rules definedabove and, preferably, both rules simultaneously.

A generator polynomial obeying the first of the rules (Hamming weight)makes it possible to generate a redundancy signaling at best the randomerrors. A generator polynomial obeying the second rule (detection of atleast 2^(s-1)−3 consecutive erroneous bits) makes it possible togenerate a redundancy signaling at best the burst errors. The parametersused in each of the aforementioned rules are adjusted according to thechosen application (environment, type of receivers, etc.).

According to one embodiment, the generator polynomial is preferablycoded on eight bits. In this case, the threshold is, for example,greater than or equal to 4. Still in the situation in which thegenerator polynomial is coded on eight bits, the latter preferablyallows the detection of at least 125 consecutive erroneous bits.

As a variant, the threshold may be greater than or equal to 3. In thiscase, the generator polynomial may allow the detection of at least 126consecutive erroneous bits.

According to one embodiment, the choice of a generator polynomial mayinclude for each polynomial belonging to a chosen set, performing afirst test in which the user verifies in parallel whether the polynomialallows the detection of a first number of consecutive erroneous bitsequal to 126 on the one hand, and of a second number of consecutiveerroneous bits equal to 125 on the other hand. In addition, for thepolynomials verifying the first test relative to the first and to thesecond number of erroneous bits, a second test may be performed in whichthe user verifies whether these polynomials allow the detection of anumber of consecutive erroneous bits either less than 126 if thepolynomial already allows the detection of 126 consecutive erroneousbits, or less than 125 erroneous bits if the polynomial already allowsthe detection of 125 consecutive erroneous bits.

For the polynomials not satisfying the second test, a third test may beperformed in which the user verifies whether the Hamming weight of themultiples of these polynomials is greater than or equal to 4. Aclassification of the polynomials satisfying the third test in a firstfamily of generator polynomials may be generated. For the polynomialsnot satisfying the third test, a fourth test may be performed in whichthe user verifies whether the Hamming weight of the multiples of thesepolynomials is greater than or equal to three. A classification of thepolynomials satisfying the fourth test in a second family of generatorpolynomials may be generated.

For example, a generator polynomial belonging to the first family maytake the form x⁷+x⁴+x²+1. A generator polynomial belonging to the secondfamily may be chosen from x⁷+x⁶+x³+x+1, x⁷+x⁶+x⁴+x+1, x⁷+x+1 orx⁷+x⁶+x⁵+x³+x.

According to another aspect, there is a system for transmitting a binaryinformation word comprising an emitter and at least one receiver coupledvia transmission circuitry, the system being capable of applying themethod as defined above.

BRIEF DESCRIPTION OF THE DRAWINGS

Other advantages and features of the various aspects will appear onexamining the detailed description of non-limiting examples and of thefigures including:

FIG. 1 illustrating a transmission system of the present invention; and

FIG. 2 illustrating as an example the choice of a generator polynomialcoded on eight bits, according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In FIG. 1, the reference SYS illustrates a binary information wordtransmission system. This system SYS comprises an emitter EM and areceiver RC. This example is not limiting and the system SYS maycomprise several receivers.

The emitter EM and the receiver RC are coupled via transmissioncircuitry MT. The emitter EM transmits to the receiver RC an informationword MI coded on r bits (in this instance 12 bits), in this example thesequence “010011101101”. Based on the information word MI, a redundancyCRC is generated. More precisely, the information word MI is transmittedto a divider DIV which carries out a Euclidian division of theinformation word MI by a generator polynomial, the features of whichwill be described in greater detail below.

The redundancy CRC is coded on s bits (s<r), in this example 3 bits“101”. The redundancy CRC is the remainder of the Euclidian division ofthe information word MI by the generator polynomial.

Formation circuitry MF then forms the message to be transmitted ME basedon the information word MI and the redundancy CRC. The redundancy iscoupled to the information word MI. To do this, the formation circuitryMF may, for example, add s “0” at the end of the information word MI(“zero padding”). Then the formation circuitry MF adds up theinformation word MI then coded on r+s bits and the redundancy CRC.

The message to be transmitted ME is therefore a sequence of s+r bits, inthis instance “010011101101101”. The message received by the receiver isreferenced ME′. It is also coded on r+s bits, the first r bitscorresponding to the received information word and the last s bitscorresponding to the redundancy.

The first r bits of the received message ME′ are then divided by thesame generator polynomial used to obtain the redundancy CRC within theemitter. This division is carried out by another divider DIVRC situatedwithin the receiver RC. This then gives a value CRC′ which is thencompared with the last s bits of the message ME′ with the aid of acomparator CMP.

If these last s bits (corresponding to the redundancy CRC) and the valueCRC′ are different (which is the case here because the fifth and eighthbits of the formation word received by the receiver RC are erroneous),the receiver is informed that the message ME′ comprises erroneous bits.

The generator polynomial used by the dividers DIV and DIVRC is chosen sothat the probability of having undetected errors during the transmissionof a message is low. To do this, the generator polynomial obeys at leastone of the two rules, namely that the Hamming weight of the multiples ofthe generator polynomial is greater than or equal to a chosen threshold,or the generator polynomial allows the detection of at least 2^(s-1)−3consecutive erroneous bits.

The calculation of the Hamming weight of the multiples of a polynomialshould be understood by those skilled in the art. The aforementionedthreshold corresponds to the minimal Hamming weight. This threshold is afunction of the number of bits of the generator polynomial. Conventionaltests make it possible to identify the acceptable thresholds for a givendegree of polynomials.

Moreover, an optimal generator polynomial withstands at best 2^(s-1)−3consecutive errors if burst errors are considered, that is to say thenumber of consecutive bits of the information message having anerroneous value.

FIG. 2 illustrates the various steps of the choice of an optimalgenerator polynomial. These steps are given for a generator polynomialcoded on eight bits. The latter are particularly suitable fortransmissions between wireless telecommunication systems (for examplemobile telephones).

Let P be a polynomial that is tested in order to know if it correspondsto a good generator polynomial as defined above. A first test, test 1,is run which includes, notably, verifying whether the polynomial Pallows the detection of at least 126 consecutive erroneous bits, that isto say 2^(s-1)−2 consecutive erroneous bits, where s=8.

The same test is run on the polynomials P but, in this case, the userverifies what allows the detection of only 125 consecutive erroneousbits, that is to say 2^(s-1)−3 consecutive erroneous bits, where s=8.

For the polynomials of which the test result is YES, a second test, test2, is run to ascertain whether the polynomial allows the detection ofless than 126 consecutive erroneous bits if test 1 relates to 126 bits,and of less than 125 consecutive erroneous bits if test 1 relates to 125bits.

If the polynomial P in question verifies these second tests, it is not acandidate to be an optimal generator polynomial. In contrast, thepolynomials not verifying this second test are then subjected to a thirdtest, test 3, to ascertain whether the Hamming weight of the multiplesof the latter is greater than or equal to 4.

If this is the case, the polynomials P are then classified in a firstfamily, FAMILY 1. Otherwise, they are subjected to another test, test 4,in order to see whether the Hamming weight of the multiples of thesepolynomials is greater than or equal to 3. If this is the case, thesepolynomials are classified in a second family, FAMILY 2. Distributed inthe table below are examples of polynomials belonging to FAMILY 1 orFAMILY 2 as defined above.

Family 1 Family 2 x⁷ + x⁵ + x⁴ + x² + x + 1 x⁷ + x + 1 x⁷ + x⁶ + x⁵ +x³ + x² + 1 x⁷ + x⁶ + 1 x⁷ + x⁵ + x + 1 x⁷ + x³ + 1 x⁷ + x⁶ + x² + 1x⁷ + x⁴ + 1 x⁷ + x⁴ + x² + 1 x⁷ + x⁵ + x⁴ + x³ + x² + x + 1 x⁷ + x⁵ +x³ + 1 x⁷ + x⁶ + x⁵ + x⁴ + x³ + x² + 1 x⁷ + x⁴ + x³ + x² + 1 x⁷ + x⁵ +x⁴ + x³ + 1 x⁷ + x⁵ + x² + x + 1 x⁷ + x⁶ + x⁵ + x² + 1 x⁷ + x⁶ + x⁵ +x³ + x² + x + 1 x⁷ + x⁶ + x⁵ + x⁴ + x² + x + 1 x⁷ + x³ + x² + x + 1 x⁷ +x⁶ + x⁵ + x⁴ + 1 x⁷ + x⁵ + x³ + x + 1 x⁷ + x⁶ + x⁴ + x² + 1 x⁷ + x⁶ +x³ + x + 1 x⁷ + x⁶ + x⁴ + x + 1

The table above lists the generator polynomials coded on eight bitsmaking it possible to have the best results, that is to say the lowestpercentage of undetected errors.

The generator polynomials x⁷+x⁶+x³+x+1 and x⁷+x⁶+x⁴+x+1 are particularlyeffective for detecting potential random errors which may arrive ontransmitters sensitive to electromagnetic interference. The polynomialsx⁷+x+1, x⁷+x⁶+1, x⁷+x³+1 and x⁷+x⁴+1 are, for their part, very effectivewhen the circuit is short, that is to say when the distance between theemitter and the receiver is short.

The example above is given in the context of a generator polynomialcoded on eight bits but the invention is absolutely not limited to thisexample. The method may be applied to the choice of a generatorpolynomial of n bits, n being any integer.

Many modifications and other embodiments will come to the mind of oneskilled in the art having the benefit of the teachings presented in theforegoing descriptions and the associated drawings. Therefore, it isunderstood that the invention is not to be limited to the specificembodiments disclosed, and that modifications and embodiments areintended to be included within the scope of the appended claims.

1-10. (canceled)
 11. A method for transmitting a binary word comprisingr bits and a cyclic redundancy check (CRC) comprising s bits, the methodcomprising: performing a Euclidian division of the binary word by agenerator polynomial of at most s bits to thereby generate the CRC; thegenerator polynomial being such that a Hamming weight of multiples ofthe generator polynomial is at least at a threshold value; andtransmitting the binary word and the CRC.
 12. A method according toclaim 11, wherein the generator polynomial comprises 8 bits.
 13. Amethod according to claim 11, wherein the threshold value is at least 4.14. A method according to claim 11, wherein the generator polynomialallows the detection of at least 125 consecutive errored bits.
 15. Amethod according to claim 11, wherein the threshold value is at least 3.16. A method according to claim 11, wherein the generator polynomialallows the detection of at least 126 consecutive errored bits.
 17. Amethod according to claim 11, wherein the generator polynomial isselected by: for each polynomial belonging to a chosen set, performing afirst test to verify whether the polynomial allows the detection of 126consecutive errored bits, and whether the polynomial allows thedetection of 125 consecutive errored bits; for each polynomial passingthe first test, performing a second test to verify whether thepolynomial allows the detection of less than 126 errored bits if thepolynomial allows the detection of 126 consecutive errored bits, andwhether the polynomial allows the detection of less than 125 erroredbits if the polynomial allows the detection of 125 consecutive erroredbits; for each polynomial failing the second test, performing a thirdtest to verify whether the Hamming weight of the multiples of thepolynomial is at least 4; classifying each polynomial passing the secondtest as belonging to a first family of generator polynomials; for eachpolynomial failing the third test, performing a fourth test to verifywhether the Hamming weight of the multiples of the polynomial is atleast 3; classifying each polynomial passing the third test as belongingto a second family of generator polynomials.
 18. A method according toclaim 17, wherein generator polynomials belonging to the first family ofgenerator polynomials take a form of x⁷+x⁴+x²+1.
 19. A method accordingto claim 17, wherein polynomials belonging to the second family ofgenerator polynomials take a form of one of x⁷+x⁶+x³+x+1, x⁷+x⁶+x⁴+x+1,x⁷+x+1, and x⁷+x⁶+x⁵+x³+x.
 20. A method for transmitting a binary wordcomprising r bits and a cyclic redundancy check (CRC) comprising s bits,the method comprising: performing a Euclidian division of the binaryword by a generator polynomial of at most s bits to thereby generate theCRC; the generator polynomial being such that the generator polynomialallows detection of at least 2^(s-1)−3 consecutive errored bits; andtransmitting the binary word and the CRC.
 21. A method according toclaim 20, wherein the generator polynomial is selected by: for eachpolynomial belonging to a chosen set, performing a first test to verifywhether the polynomial allows the detection of 126 consecutive erroredbits, and whether the polynomial allows the detection of 125 consecutiveerrored bits; for each polynomial passing the first test, performing asecond test to verify whether the polynomial allows the detection ofless than 126 errored bits if the polynomial allows the detection of 126consecutive errored bits, and whether the polynomial allows thedetection of less than 125 errored bits if the polynomial allows thedetection of 125 consecutive errored bits; for each polynomial failingthe second test, performing a third test to verify whether the Hammingweight of the multiples of the polynomial is at least 4; classifyingeach polynomial passing the second test as belonging to a first familyof generator polynomials; for each polynomial failing the third test,performing a fourth test to verify whether the Hamming weight of themultiples of the polynomial is at least 3; classifying each polynomialpassing the third test as belonging to a second family of generatorpolynomials.
 22. A method according to claim 21, wherein generatorpolynomials belonging to the first family of generator polynomials takea form of x⁷+x⁴+x²+1.
 23. A method according to claim 21, whereinpolynomials belonging to the second family of generator polynomials takea form of one of x⁷+x⁶+x³+x+1, x⁷+x⁶+x⁴+x+1, x⁷+x+1, and x⁷+x⁶+x⁵+x³+x.24. A system for transmitting a binary word comprising r bits and acyclic redundancy check (CRC) comprising s bits, the system comprising:CRC generation circuitry for performing a Euclidian division of thebinary word by a generator polynomial of at most s bits to therebygenerate the CRC, the generator polynomial being such that a Hammingweight of multiples of the generator polynomial is at least at athreshold value; and a transmitter to transmit the binary word and theCRC.
 25. A system according to claim 24, wherein the generatorpolynomial comprises 8 bits.
 26. A system according to claim 24, whereinthe threshold value is least
 4. 27. A system according to claim 24,wherein the generator polynomial allows the detection of at least 125consecutive errored bits.
 28. A system according to claim 24, whereinthe threshold value is at least
 3. 29. A system according to claim 24,wherein the generator polynomial allows the detection of at least 126consecutive errored bits.
 30. A system according to claim 24, whereinthe CRC generation circuitry selects the generator polynomial by: foreach polynomial belonging to a chosen set, performing a first test toverify whether the polynomial allows the detection of 126 consecutiveerrored bits, and whether the polynomial allows the detection of 125consecutive errored bits; for each polynomial passing the first test,performing a second test to verify whether the polynomial allows thedetection of less than 126 errored bits if the polynomial allows thedetection of 126 consecutive errored bits, and whether the polynomialallows the detection of less than 125 errored bits if the polynomialallows the detection of 125 consecutive errored bits; for eachpolynomial failing the second test, performing a third test to verifywhether the Hamming weight of the multiples of the polynomial is atleast 4; classifying each polynomial passing the second test asbelonging to a first family of generator polynomials; for eachpolynomial failing the third test, performing a fourth test to verifywhether the Hamming weight of the multiples of the polynomial is atleast 3; classifying each polynomial passing the third test as belongingto a second family of generator polynomials.
 31. A system according toclaim 30, wherein polynomials belonging to the first family of generatorpolynomials take a form of x⁷+x⁴+x²+1.
 32. A system according to claim30, wherein polynomials belonging to the second family of generatorpolynomials take a form of one of x⁷+x⁶+x³+x+1, x⁷+x⁶+x⁴+x+1, x⁷+x+1,and x⁷+x⁶+x⁵+x³+x.
 33. A system for transmitting a binary wordcomprising r bits and a cyclic redundancy check (CRC) comprising s bits,the system comprising: CRC generation circuitry for performing aEuclidian division of the binary word by a generator polynomial of atmost s bits to thereby generate the CRC, the generator polynomial beingsuch that the generator polynomial allows detection of at least2^(s-1)−3 consecutive errored bits; and a transmitter to transmit thebinary word and the CRC.
 34. A system according to claim 33, wherein theCRC generation circuitry selects the generator polynomial by: for eachpolynomial belonging to a chosen set, performing a first test to verifywhether the polynomial allows the detection of 126 consecutive erroredbits, and whether the polynomial allows the detection of 125 consecutiveerrored bits; for each polynomial passing the first test, performing asecond test to verify whether the polynomial allows the detection ofless than 126 errored bits if the polynomial allows the detection of 126consecutive errored bits, and whether the polynomial allows thedetection of less than 125 errored bits if the polynomial allows thedetection of 125 consecutive errored bits; for each polynomial failingthe second test, performing a third test to verify whether the Hammingweight of the multiples of the polynomial is at least 4; classifyingeach polynomial passing the second test as belonging to a first familyof generator polynomials; for each polynomial failing the third test,performing a fourth test to verify whether the Hamming weight of themultiples of the polynomial is at least 3; classifying each polynomialpassing the third test as belonging to a second family of generatorpolynomials.
 35. A system according to claim 34, wherein polynomialsbelonging to the first family of generator polynomials take a form ofx⁷+x⁴+x²+1.
 36. A system according to claim 34, wherein polynomialsbelonging to the second family of generator polynomials take a form ofone of x⁷+x⁶+x³+x+1, x⁷+x⁶+x⁴+x+1, x⁷+x+1, and x⁷+x⁶+x⁵+x³+x.